A079164 Twin-primorial numbers: running products of twin primes.

3, 15, 75, 525, 5775, 75075, 1276275, 24249225, 703227525, 21800053275, 893802184275, 38433493923825, 2267576141505675, 138322144631846175, 9820872268861078425, 716923675626858725025, 72409291238312731227525

Offset

1,1

Comments

The sum of the reciprocals converges to 0.4154254016622336549103692152614908366885449298862362851444631680740051...

Links

Amiram Eldar, Table of n, a(n) for n = 1..309

Example

The first two twin primes are 3 and 5, so the first term is 3 and the second term is 15.  The next two twin primes are 5 and 7, so the third term is 5*15=75 and the fourth term is 75*7=525

Mathematica

Rest[FoldList[Times, 1, Flatten[Select[Partition[Prime[Range[30]], 2, 1], Last[#]-First[#]==2&]]]] (* Harvey P. Dale, Mar 16 2011 *)

Prog

(PARI) twprfact(n) = {sr=0; tp = vector(10000); k=1; forprime(j = 3, n, if(nextprime(j+1)-j == 2, tp[k] = j; tp[k+1] = j+2; k+=2; ); ); for(j=1, k-1, y=1; for(i = 1, j, y*=tp[i]; ); print1(y", "); sr+=1.0/y; ); print(); print(sr); }

Crossrefs

Partial products of A077800.

Sequence in context: A000266 A294340 A059838 * A240941 A047015 A322186

Adjacent sequences: A079161 A079162 A079163 * A079165 A079166 A079167

Keyword

nonn

Author

Cino Hilliard, Feb 03 2003

Extensions

Definition clarified and example provided by Harvey P. Dale, Mar 16 2011

Status

approved